The geometry of voting power: Weighted voting and hyper-ellipsoids

Suppose legislators represent districts of varying population, and their assembly's voting rule is intended to implement the principle of one person, one vote. How should legislators' voting weights appropriately reflect these population differences? An analysis requires an understanding of the relationship between voting weight and some measure of the influence that each legislator has over collective decisions. We provide three new characterizations of weighted voting that embody this relationship. Each is based on the intuition that winning coalitions should be close to one another. The locally minimal and tightly packed characterizations use a weighted Hamming metric. Ellipsoidal separability employs the Euclidean metric: a separating hyper-ellipsoid contains all winning coalitions, and omits losing ones. The ellipsoid's proportions, and the Hamming weights, reflect the ratio of voting weight to influence, measured as Penrose–Banzhaf voting power. In particular, the spherically separable rules are those for which voting powers can serve as voting weights.     

Purchasing power parity and real factors

It is acknowledged that purchasing power parity (PPP) fails in empirical tests. The position adopted is that real factors are an omitted variable from the PPP relationship and are the cause of divergences from PPP. The real exchange rate as being determined by supply and demand shift factors (as in Stockman, 1987 and Neary, 1988) is modelled. We then empirically estimate a real exchange rate equation and use the fitted value as a generated regressor in tests of PPP. It is demonstrated that when changes in the real exchange rate are incorporated into the PPP relationship, PPP improves.     

Party voting discipline and the power of parties, legislators and states

We examine the distribution of decision-making power among the principal actors of a federal legislative system; parties, legislators, and constituencies. We are especially interested in how the balance of power between legislators and constituencies depends on the voting discipline exercised by the parties.We derive power measures that are related to the Banzhaf-Coleman index of decision-making power and illustrate with a simple example. Our power measures are novel because they are based on an explicit representation of party voting discipline as well as the structural properties of the decision-making process, whereas previous analyses concentrate on structurally determined power alone.     

Formal and real ownership structure of the Polish economy: state-owned versus state-controlled enterprises

This article analyses the difference between the state’s formal and real shares in the Polish economy. We identify two basic types of corporate control exercised by the state over enterprises through ownership (in the case of majority ownership) and non-ownership tools (in the case of minority ownership). Consequently, we distinguish between two types of state enterprises: state-owned enterprises (SOEs) and state-controlled enterprises (SCEs). In post-communist economies, SCEs mainly originate from so-called reluctant privatisation, in which the transfer of ownership rights takes place without the appropriate transfer of control rights. We discuss the tools of non-ownership control used by the state. Our estimates of the real share of state enterprises in the Polish economy (which include both SOEs and SCEs) show that it is almost two times higher than the formal share (only SOEs). The share of state enterprises is also highest in the group of Poland’s largest and most important firms. We conclude that the real importance of state enterprises in the Polish economy is much higher than might be expected if only the formal share of state ownership is taken into account.     

Information and strategic voting

We theoretically and experimentally study voter behavior in a setting characterized by plurality rule and mandatory voting. Voters choose from three options. We are interested in the occurrence of strategic voting in an environment where Condorcet cycles may occur and focus on how information about the preference distribution affects strategic behavior. We also vary the relative importance of the second preferred option. Quantal response equilibrium analysis is used to analyze the game and derive predictions. Our results indeed show that strategic voting arises. Its extent depends on (i) information availability; (ii) the relative importance of the intermediate candidate; (iii) the electorate’s relative support for one’s preferred candidate; (iv) the relative position of the plurality-supported candidate in one’s preference ordering. Our results show that information serves as a coordination device where strategic voting does not harm the plurality-preferred candidate’s chances of winning.     

Deliberative voting

We analyze a model of jury decision making in which jurors deliberate before casting their votes. We consider a wide range of voting institutions and show that deliberations render these equivalent with respect to the sequential equilibrium outcomes they generate. In particular, in the context of a jury setup, all voting rules excluding the two types of unanimity rules (one requiring a unanimous consensus to acquit, one requiring a unanimous consensus to convict) induce the same set of equilibria outcomes. We show the robustness of our results with respect to several restrictions on communication protocols and jurors’ strategies. Furthermore, we demonstrate that our observations extend to practically all of the voting structures commonly studied in the voting literature. The paper suggests the importance of accounting for communication in models of collective choice.     

Approval voting reconsidered

Summary. The merit of approval voting has been widely discussed in the past 25 years. The distinct property of this rule is the extent of flexibility it allows; any voter can approve as many alternatives/candidates as he wishes. Nevertheless, this advantage is the very reason for two drawbacks of approval voting: its extreme vulnerability to majority decisiveness (Theorem 1) and its extreme vulnerability to erosion of the majority principle (Theorem 2). On the one hand, under some feasible voting strategies any majority of more than 1/2 of the voters can guarantee the selection of its most favorable candidate, regardless of the preferences of the other voters. On the other hand, under alternative voting strategies even the largest majority cannot impose its common most preferred candidate. A simultaneous resolution of the two problems is possible by restricted approval voting (RAV), a voting rule that allows partial voter flexibility by restricting the minimal and maximal number of candidates that can be approved. Our main result (Theorem 3) clarifies how the foregone flexibility in voters sovereignty mitigates the above mentioned drawbacks under sincere and insincere coordinated voting. Our findings suggest a new possible justification of a particular voting rule which is based on the significance assigned to three considerations: the advantages of voters flexibility, immunity to majority decisiveness and immunity to erosion of the majority principle. Such justification can provide a possible explanation to the prevalent use of some special cases of RAV, notably, of the plurality rule and of approval voting.Received: 8 October 2003, Revised: 17 June 2004, JEL Classification Numbers: D71, D72. Correspondence to: Shmuel NitzanWe are indebted to Steve Brams, Remzi Sanver and an anonymous referee for their very useful comments and suggestions.     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

Strategic delegation and voting rules

The selection of political representatives depends on the political system. Principals, such as voters or districts, may benefit by strategically electing representatives different from themselves. While a status-quo biased delegate may be a better negotiator, an enthusiastic representative has a better chance of being included in the majority coalition. A larger majority requirement leads to “conservative” delegation and hence a status quo bias; a poor minority protection does the opposite. Through strategic delegation, the political system also determines whether centralization or decentralization is beneficial.     

Size approval voting

We propose a new class of voting procedures, called Size Approval Voting, according to which, the effective weight of a vote from a given individual depends on how many other candidates that individual votes for. In particular, weights are assumed to be non-negative and weakly decreasing in the number of approved candidates. Then, for a given profile of individual votes, all candidates with the maximal sum of weighted votes are elected. We show in our axiomatic analysis that the family of all Size Approval Voting procedures is characterized by a set of natural properties.     

Candidate stability and probabilistic voting procedures

Summary. We extend the analysis of Dutta, Jackson and Le Breton (Econometrica, 2001) on strategic candidacy to probabilistic environments. For each agenda and each profile of voters preferences over running candidates, a probabilistic voting procedure selects a lottery on the set of running candidates. Assuming that candidates cannot vote, we show that random dictatorships are the only unanimous probabilistic voting procedures that never provide unilateral incentives for the candidates to withdraw their candidacy at any set of potential candidates. More flexible probabilistic voting procedures can be devised if we restrict our attention to the stability of specific sets of potential candidates.Received: 4 February 2003, Revised: 14 September 2004, JEL Classification Numbers: D71, D72.This is a revised version of a chapter of my Ph.D. Dissertation submitted to the Universitat Autónoma de Barcelona. I am indebted to my supervisor Salvador Barberá for his advice and constant support. I am grateful to Dolors Berga and an anonymous referee for their detailed comments and suggestions. I thank José Alcalde, Walter Bossert, Bhaskar Dutta, Lars Ehlers, Jordi Massó, Diego Moreno, Clara Ponsatí, Yves Sprumont, and William Thomson for many helpful comments and discussions. I thank the hospitality of the C.R.D.E. at the Université de Montréal and the Department of Economics of the University of Warwick where parts of this research were conducted. Financial support through Research Grant 1998FI00022 from Comissionat per Universitats i Recerca, Generalitat de Catalunya, Research Project PB98-870 from the Ministerio de Ciencia y Tecnología, and Fundación Barrié de la Maza is gratefully acknowledged.     

Sequential voting with abstention

Dekel and Piccione [2000. Sequential voting procedures in symmetric binary elections. J. Polit. Economy 108, 34–55] have proven that information cascades do not necessarily affect the properties of information aggregation in sequential elections: under standard conditions, any symmetric equilibrium of a simultaneous voting mechanism is also an equilibrium of the correspondent sequential mechanism. We show that when voters can abstain, these results are sensitive to the introduction of an arbitrarily small cost of voting: the set of equilibria in the two mechanisms are generally disjoint; and the informative properties of the equilibrium sets can be ranked. If an appropriate q-rule is chosen, when the cost of voting is small the unique symmetric equilibrium of the simultaneous voting mechanism dominates all equilibria of the sequential mechanism.     

Gender preference gaps and voting for redistribution

Experimental Economics - There is substantial evidence that women tend to support different policies and political candidates than men. Many studies also document gender differences in a variety of...     

Majority voting on restricted domains

In judgment aggregation, unlike preference aggregation, not much is known about domain restrictions that guarantee consistent majority outcomes. We introduce several conditions on individual judgments sufficient for consistent majority judgments. Some are based on global orders of propositions or individuals, others on local orders, still others not on orders at all. Some generalize classic social-choice-theoretic domain conditions, others have no counterpart. Our most general condition generalizes Sen's triplewise value-restriction, itself the most general classic condition. We also prove a new characterization theorem: for a large class of domains, if there exists any aggregation function satisfying some democratic conditions, then majority voting is the unique such function. Taken together, our results support the robustness of majority rule.     

Necessity conditions in voting theory

In this paper we take some concepts of necessity conditions in voting theory first developed by Inada, Sen, and Pattanaik and refine those concepts to deal with the more commonly discussed case of fixed numbers of voters. These new concepts are then applied to the study of domain restrictions designed to yield quasitransitive and transitive social preference relations. Along the way, a conjecture of Pattanaik is settled.     

Victory margins and the paradox of voting

This paper addresses a simple question: why do people vote? Though simple, this question remains unanswered despite the considerable attention it has received. In this paper, I show that purely rational–instrumental factors explain a large fraction of turnout variations, provided that the effect of the margin of victory on implemented policy is considered. I extend Myerson's models of elections based on Poisson games, and show that, when platforms are responsive to vote shares, the predictions of the model become consistent with several stylized facts, including the secular fall in turnout rates in the US.